Images of Rational Maps of Projective Spaces
Images of Rational Maps of Projective Spaces
复制标题
射影空间有理映射的图像
DOI：
10.1093/imrn/rnx003
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Binglin Li
中科院分区：
文献类型：
--
作者：
Binglin Li
考虑一个从射影空间到射影空间乘积的有理图，由一组线性投影引起。在极限线性级数和Abel-Jacobi映射理论的启发下，利用模函子和初始退化相结合的方法研究了有理映射象闭包的基本性质。首先给出了线性子空间交点维数的一个多次公式，并证明了它是Cohen-Macaulay公式。最后，我们计算它的希尔伯特多项式。
Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the closure of the image of the rational map using a combination of techniques of moduli functors and initial degenerations. We first give a formula of multi-degree in terms of the dimensions of intersections of linear subspaces and then prove that it is Cohen-Macaulay. Finally, we compute its Hilbert polynomials.